Yes, it's okay to repot the plant when it has small fruit. However, the disturbance to the roots might cause the plant to drop some or all of the immature tomatoes.
If the plant is in a container, though, and its roots are constricted, i.e. root bound, then failure to repot will cost you not only these earliest fruits, but the entire plant.
If you repot the plant and it drops the fruit, it will bloom again. As long as the temperature is right and the flowers get pollinated (I gently shake my tomato plants every day when they're blooming to ensure pollination), it will soon set more fruit.
Neem oil is fine to use, but I'm not sure it will deter aphids. I think the leaves have to be ingested, such as eaten by a caterpillar, for it to be effective beyond being sprayed directly on the insects. The soap spray only works on direct contact and has to be repeated about 4 times, every 5 to 7 days, in order to kill any survivors or juveniles. Aphids are sometimes brought to plants by ants. If you see ants on your tomato plants, treat for them, or you'll be fighting a never ending battle with the aphids.
"Isn't it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too?" - Douglas Adams